Our result for FePc in the relaxed geometry
corresponds to the black full line of Fig. REF  and reproduces the main features of the
observed differential conductance except for some asymmetry in the experiments,
which we neglect in this subsection as explained above.
As the molecule is raised from the substrate by the attractive force of the STM tip, the Kondo
coupling to the substrate is reduced [1]}. We assume that both exchange coupling constants
\(J_\tau \)  are reduced by the same factor \(f\) 
because the same power-law dependence of the tunneling parameters \(V_\tau \)  with the distance is expected.
between the localized 3d orbitals and the extended conduction states [2]}. As this
factor \(f\)  decreases from 1, the spectral density flattens and the dip broadens so that the
line-shape becomes similar to that observed in single-channel Kondo systems with magnetic
anisotropy [3]}, [4]}. The exact same trend is observed experimentally
[1]}. For very small \(f\) , there should be two sharp steps at the unrenormalized
threshold for inelastic spin-flip excitations (\(\omega =\pm D\) ); in our
calculations they are overbroadened due to technical reasons that limit the resolution of the NRG
at large energies [6]}.
